On tadpole relations via Verdier specialization

TL;DR

This paper mathematically derives Chern class identities related to D3-brane tadpole relations in F-theory and type IIB string theory using Verdier specialization, revealing their geometric origin.

Contribution

It introduces a purely mathematical approach to derive tadpole relations via Verdier specialization, connecting physics identities to algebraic geometry.

Findings

Chern class identities correspond to Verdier's specialization formula

All weak coupling limit identities are geometric manifestations of Verdier specialization

Provides a rigorous mathematical foundation for physics-derived tadpole relations

Abstract

Using the construct of "Verdier specialization", we provide a purely mathematical derivation of Chern class identities which upon integration yield the D3-brane tadpole relations coming from the equivalence between F-theory and associated weakly coupled type IIB orientifold limits. In particular, we find that all Chern class identities associated with weak coupling limits appearing in the physics literature are manifestations of a relative version of Verdier's specialization formula.